Yang-Mills theory on noncommutative space: does it exist?

Abstract

I revisit a basic question about the noncommutative Yang-Mills theory: if it exists or not, or more precisely, whether a nonperturbative formulation exists. As the most promising approach, I consider a formulation based on matrix models. It is explained that the existence of the noncommutative Yang-Mills theory is closely related to the Eguchi-Kawai equivalence. I argue that supersymmetric noncommutative Yang-Mills theory can be defined straightforwardly. Non-supersymmetric theories, such as QCD and pure bosonic theories, can presumably be defined, by modifying the ultraviolet and infrared behaviors appropriately.

Proceedings of the Corfu Summer Institute 2015 "School and Workshops on Elementary Particle Physics and Gravity", 1-27 September 2015, Corfu, Greece. v2: a comment on an important reference has been added